When a star orbits another (which applies to about 70% of the stars in our milky way) one can derive mechanical data, such as revolution period or masses of this dumbbell-shaped system, by observing the motion of the brighter star relative to the background. The stars revolve around their common centre of gravity revealing their existence through regular wobbling.
Because a planet has a much smaller mass compared to the star, the motion amplitude of the star is very small. If the configuration of both objects is favourable (from the point of view on earth; see figure 1) it is also possible to discover such a system by detecting the change of velocity of the star using Doppler’s effect.
For instance, the star 51 Pegasi has a velocity that is 60 m/s higher when it approaches the earth compared to the velocity when it turns away from it 2.1 days later. By means of the celestial mechanics equations, one can deduce from these data the mass of the exoplanet and its distance from the star, i.e. its so-called semi-major axis. Here 51b Pegasi differs clearly from our nine planets: Its orbital period of 4.2 days is 20 times shorter than Mercury’s, and its semi-major axis is only 4% of the earth’s semi-major axis. There is no planet in our system which is so close to the sun! Only its mass is familiar to us: the mass of 51b Pegasi is about half of Jupiter’s.
Until 2004, slightly less than 2000 solar systems have been investigated. 120 of them possess planets that resemble Jupiter (as described earlier, with circulation periods between 2.5 days and several years and masses between 10% and up to 2000% of Jupiter’s mass). Earth-like planets cannot be detected by using the so-called radial-velocity method. An “exoearth” would only cause a change of velocity of approximately 0.08 m/s of its star. Such a small velocity change is smaller by one or two order of magnitude compared to the "jitter" of the stellar velocity caused by the magnetic disturbances in its atmosphere.

Another method, the so-called transit method, also presupposes that the straight line earth-star is more or less parallel to the plane that contains the exoplanet and the star. This method is based on the transit of the planet, as figure 1 shows:

Figure 1: The planet’s crossing causes a slight darkening.

Here one makes use of the fact that the planet crosses the star once in a revolution. During this time, the planet shields a particular percentage of the stellar in our direction. If the planet’s radius is similar to Jupiter’s, then this fraction is about one percent.
This luminosity drop of 0.01 is easily detectable and corresponds to the proportion of the planet’s area to the star’s area.

Figure 2: The light curve of HD209458b (period of revolution = 3.5 days, radius = 1.4Rjup, mass = 0.69Mjup)

Fig. 2 shows a typical transit of a Jupiter-like exoplanet. One can see clearly that the intensity decreases by about 2% as soon as the planet travels across the star. This covering only lasts for a few hours. One can calculate the planet’s density of 310 kg/m3 from the data shown in the figure (compared to the density of water: 1000 kg/m3), therefore one can conclude that HD209458b must be a gaseous planet, like Jupiter. Meanwhile, the experimental astrophysicists master this method so well that they are able to deduce the planet’s atmosphere from the intensity brakes of the different wavelengths! This way, they were able detect hydrogen, carbon and oxygen in the atmosphere of HD209458b.
The experiments and observations in this field will probably bring to light many more surprises, e.g. the detectionof moons orbiting exoplanets by the study of the time of transit. Even a micro-lensing effect has apparently been detected: According to Einstein’s relativity theory, a star (that is orbited by a planet) slightly bends the light coming from distant star, just like a convex lens. The change of the magnitude of the distant star luminosity could allow the detection of planets with masses as small as the Earth mass.

In future, spectrographs will improve and mankind will spot many more exoplanet systems. But earth-like planets cause a signal depth of only 1/10000 and their existence will not be proved until the planned experiments COROT (2006) and Kepler (2007) are carried out. Both instruments will investigate more than 100,000 stars. It will be fascinating to see the outcome!

Dr. Hansjörg Friedli

PS: The sensational discovery of the group from Geneva around Michel Mayor has given us a foretaste of the future quest for exoplanets. In August 2004, they published the discovery of an earth-like planet in the constellation Altar in the magazine “Astronomy and Astrophysics.” This planet orbiting the star µ Arae (which is visible to the naked eye) is “only “ 14 times heavier than the earth, it consists most likely of stone, and it is considered the lightest exoplanet known today! (N. Santos. et. al., 2004, A&A, 417, L19)

Michel Mayor and Peter Fricker at the Ceremony